List questions from compactness

Published on 11 Apr 2026 - 7:48

46

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Set of points at which a function coincides with its convexification is compact?

Published on 11 Apr 2026 - 0:26

336

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Does there exist non-compact metric space $X$ such that, any continuous function from $X$ to any Hausdorff space is a closed map?

Published on 11 Apr 2026 - 18:49

594

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When is the dual ball of $L_1(\mu)$ weak*-sequentially compact?

Published on 12 Apr 2026 - 11:55

104

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The square $S := [- R, R] \times [-R, R]$ is a compact subset of $\Bbb R^2$.

Published on 11 Apr 2026 - 21:11

55

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Negate a proposition with quantifier?

Published on 12 Apr 2026 - 15:36

2.8k

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In a Hausdorff space the intersection of a chain of compact connected subspaces is compact and connected

Published on 12 Apr 2026 - 10:31

220

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Bounded set that is not closed nor compact

Published on 09 Apr 2026 - 16:01

1.3k

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Is any compact, path-connected subset of $\mathbb{R}^n$ the continuous image of $[0,1]$?

Published on 10 Apr 2026 - 6:40

120

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Is Alexandroff duplicate compact?

Published on 08 Apr 2026 - 17:02

77

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Is compact $T_1$ topological space hausdorff?

Published on 12 Apr 2026 - 8:45

755

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Proving subsets of $l^{\infty}$ are compact

Published on 11 Apr 2026 - 17:42

649

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Spaces in which "$A \cap K$ is closed for all compact $K$" implies "$A$ is closed."

Published on 11 Apr 2026 - 22:54

1k

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Hilbert Space is not locally compact.

Published on 10 Apr 2026 - 17:13

184

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Normal space is compact

Published on 08 Apr 2026 - 19:14

List Question

Compactness result

Set of points at which a function coincides with its convexification is compact?

Does there exist non-compact metric space $X$ such that, any continuous function from $X$ to any Hausdorff space is a closed map?

When is the dual ball of $L_1(\mu)$ weak*-sequentially compact?

The square $S := [- R, R] \times [-R, R]$ is a compact subset of $\Bbb R^2$.

Negate a proposition with quantifier?

In a Hausdorff space the intersection of a chain of compact connected subspaces is compact and connected

Bounded set that is not closed nor compact

Is any compact, path-connected subset of $\mathbb{R}^n$ the continuous image of $[0,1]$?

Is Alexandroff duplicate compact?

Is compact $T_1$ topological space hausdorff?

Proving subsets of $l^{\infty}$ are compact

Spaces in which "$A \cap K$ is closed for all compact $K$" implies "$A$ is closed."

Hilbert Space is not locally compact.

Normal space is compact

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